Question

In the adjoining figure, AD/BD = AE/EC and ∠BDE = ∠CED, prove that △ABC is an isosceles triangle.

In the adjoining figure, △CAB is a right triangle, right angled at A and AD ⊥ BC. Prove that △ADB ~ △CDA. Further, if BC = 10 cm and CD = 2 cm, find the length of AD.

State the basic proportionality theorem. Use the theorem to do the following : In △ABC, AD is the angle bisector of angle A. BA is produced to E such that CE ∥ AD. Prove that BD/DC = BA/AC.

State the converse of basic proportionality theorem. Also find BF/FC in the following figure, given that AB∥DC∥EF and AE/ED = 2/3. Also, find the length of EF if AB = 10 cm and DC = 15 cm.